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Explain solution RD Sharma class 12 chapter Differential Equations exercise 21.7 question 36 maths

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Answer: \tan y=\frac{\sin 2 x}{2}+c

Hint: Separate the terms of x and y and then integrate them.

Given: \frac{d y}{d x}=\left(\cos ^{2} x-\sin ^{2} x\right) \cos ^{2} y

Solution: \frac{d y}{d x}=\left(\cos ^{2} x-\sin ^{2} x\right) \cos ^{2} y

        \begin{aligned} &\frac{d y}{\cos ^{2} y}=\left(\cos ^{2} x-\sin ^{2} x\right) d x \\\\ &\frac{d y}{\cos ^{2} y}=\cos 2 x d x \end{aligned}

          Integrating both sides

        \begin{aligned} &\int \sec ^{2} y d y=\int \cos 2 x d x \\\\ &\tan y=\frac{\sin 2 x}{2}+c \end{aligned}

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